Homotopy of non-modular partitions and the Whitehouse module

DOI10.1023/A:1018648219348zbMath0930.05099OpenAlexW1530540531MaRDI QIDQ1301860

Sheila Sundaram

Publication date: 30 January 2000

Published in: Journal of Algebraic Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1023/a:1018648219348

zbMATH Keywords

posethomologyorder complexgroup representationhomotopyCohen-Macaulay propertyset partitionpartition latticehomology modulesWhitehouse representation

Mathematics Subject Classification ID

Partitions of sets (05A18) Representations of finite symmetric groups (20C30)

Related Items

A type \(B\) analog of the Whitehouse representation, Discretized configurations and partial partitions, On configuration spaces and Whitehouse's lifts of the Eulerian representations, Partition complexes, duality and integral tree representations, A homotopy equivalence for partition posets related to liftings of \(S_{n-1}\)-modules to \(S_n\), The integral tree representation of the symmetric group, On the topology of two partition posets with forbidden block sizes, The Bergman complex of a matroid and phylogenetic trees, The pre-WDVV ring of physics and its topology

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Some combinatorial and algebraic properties of Coxeter complexes and Tits buildings
• Topological results in combinatorics
• Cohen-Macaulay ordered sets
• Homotopy type and Euler characteristic of partially ordered sets
• The fixed-point partition lattices
• Some aspects of groups acting on finite posets
• Homology of certain sets of 2-subgroups of symmetric groups
• Homotopy properties of the poset of nontrivial p-subgroups of a group
• Complexes of not \(i\)-connected graphs
• General lexicographic shellability and orbit arrangements
• The homology representations of the symmetric group on Cohen-Macaulay subposets of the partition lattice
• Cohen-Macaulay connectivity and geometric lattices
• A basis for the homology of the \(d\)-divisible partition lattice
• Otter's method and the homology of homeomorphically irreducible \(k\)-trees
• Hidden \(\Sigma_{n+1}\)-actions
• The tree representation of \(\Sigma_{n+1}\)
• A decomposition of the group algebra of a finite Coxeter group
• Shellable and Cohen-Macaulay Partially Ordered Sets
• Balanced Cohen-Macaulay Complexes
• A $q$-deformation of a trivial symmetric group action
• Shellable Nonpure Complexes and Posets. I